f(x)=2x^3+1

Question

Find the inverse of the function. Is the invere a function?

Answer 1

y = 2x^3 + 1

y - 1 = 2x^3

(y-1)/2 = x^3

( (y-1) / 2 ) ^ (1/3) = x

Inverse:  y = ( (x-1) / 2 ) ^ (1/3)

The inverse is a function because, for each value of x, there is only one value of y.

This is another way of saying it passes the vertical line test- for each possible value of x, a vertical line only crosses the function once.